An agent (who may or may not want to be found) is located in one of two boxes. At time 0 suppose that he is in box B. With probability p he wishes to be found, in which case he has been asked to stay in box B. With probability 1-p he tries to evade the searcher, in which case he may move between boxes A and B. The searcher looks into one of the boxes at times 1, 2, 3, … . Between each search the agent may change boxes if he wants. The searcher is trying to minimise the expected time to discovery. The agent is trying to minimise this time if he wants to be found, but trying to maximise it otherwise. This paper finds a solution to this game (in a sense defined in the paper), associated strategies for the searcher and each type of agent, and a continuous value function v(p) giving the expected time for the agent to be discovered. The solution method (which is to solve an associated zero-sum game) would apply generally to this type of game of incomplete information.
